The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0  0  X  X  X  X  1 X^2  1  1  X  X  0  1  1  X  X  0  X  0  1  X  X  X  1  0  1  1 X^2  1  1 X^2  X  1  0 X^2  1  X  X  1  X X^2  1  X  X  X
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  0 X^2+X  X X^2  X X^2+X X^2  X X^2  0 X^2+X X^2+X X^2  0  X  0  X  0  X X^2 X^2 X^2 X^2  0 X^2+X  X  X  X  0 X^2+X X^2+X X^2  X  X X^2 X^2+X X^2+X X^2+X X^2  X X^2 X^2 X^2  X  X  X X^2  X  X  0  0  X X^2  X X^2+X X^2  0 X^2 X^2 X^2  X  X X^2 X^2  X  0 X^2+X  X  0  0  X X^2+X X^2+X X^2 X^2  X  0  X  0
 0  0  X  0  X  X X^2+X  0  0  0  X X^2  X X^2+X X^2 X^2+X  0  0 X^2+X  0  X X^2+X  X X^2 X^2+X X^2+X  0  0  X  X  X X^2 X^2  0 X^2 X^2+X X^2+X  0  0 X^2+X X^2+X  X X^2+X X^2+X X^2+X X^2+X  X  X X^2+X X^2 X^2+X  0 X^2+X  X X^2 X^2+X X^2+X  X  0 X^2  0 X^2 X^2+X X^2 X^2+X  0 X^2+X X^2  X  0 X^2  X X^2 X^2 X^2 X^2 X^2 X^2 X^2+X  0  X  X  X X^2+X X^2 X^2+X  X  X  X X^2+X  X  X
 0  0  0  X  X  0 X^2+X  X  0  X  0  X X^2+X X^2+X X^2 X^2  0 X^2  X  X  0  0  X X^2+X X^2 X^2+X  0 X^2+X X^2  X X^2  0 X^2+X  X X^2+X X^2  X X^2 X^2 X^2+X X^2+X X^2 X^2+X  0  0  0 X^2+X  0 X^2+X X^2  X  X  0 X^2+X X^2+X X^2  0 X^2  0  0  X  0  0  X X^2  X X^2+X X^2+X  X  X  0  X  0 X^2 X^2+X X^2+X X^2+X  0  0  X X^2+X X^2 X^2  0  X X^2  0  X X^2  X X^2 X^2+X
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0

generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+84x^79+145x^80+232x^81+250x^82+334x^83+435x^84+508x^85+700x^86+696x^87+881x^88+966x^89+1104x^90+1234x^91+1272x^92+1296x^93+1155x^94+1030x^95+852x^96+752x^97+568x^98+470x^99+356x^100+264x^101+224x^102+200x^103+113x^104+66x^105+73x^106+42x^107+32x^108+12x^109+15x^110+6x^111+6x^112+4x^114+1x^116+2x^118+2x^120+1x^122

The gray image is a linear code over GF(2) with n=368, k=14 and d=158.
This code was found by Heurico 1.16 in 42.7 seconds.